Optical transmission line and optical transmission system including the same

ABSTRACT

The present invention relates to an optical transmission line comprising a structure for effectively lowering both of nonlinearity and dispersion slope, and an optical transmission system including the same. The optical transmission line comprises, as a repeatered transmission line disposed between stations, a single-mode optical fiber having a zero-dispersion wavelength in a 1.3-μm wavelength band and a dispersion-compensating optical fiber for compensating for the chromatic dispersion of the single-mode optical fiber. The optical transmission line has an average dispersion slope S ave  of −0.0113 ps/nm 2 /km or more but 0.0256 ps/nm 2 /km or less at a wavelength of 1550 nm, and an equivalent effective area EA eff  of 50 μm 2  or more at the wavelength of 1550 nm, whereas the average dispersion slope S ave  and the equivalent effective area EA eff  are designed so as to satisfy a predetermined condition such that the bending loss falls within a permissible range of 2 dB/m or more but 10 dB/m or less.

This is a continuation in part of Ser. No. 09/792,059 filed Feb. 26, 2001 now U.S. Pat. No. 6,496,631.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical transmission line employed in a repeatered transmission line disposed between stations, and an optical transmission system including the same.

2. Related Background Art

Wavelength division multiplexing (WDM) optical transmission utilizing signals of a plurality of channels included in a 1.55-μm wavelength band enables high-speed, large-capacity information transmissions. Factors restricting the transmission capacity in this WDM optical transmission include the nonlinearity and dispersion slope of the optical transmission line. Therefore, in order to improve the performance of a WDM optical transmission system, it is important to suppress the nonlinearity of the optical transmission line (e.g., by increasing its effective area) and lower the dispersion slope of the optical transmission line.

Proposed as an optical transmission line aimed at suppressing the nonlinearity and lowering the dispersion slope as such is an optical transmission line having a configuration in which a single-mode optical fiber and a dispersion-compensating optical fiber are connected to each other. The single-mode optical fiber (hereinafter referred to as SMF) has a zero-dispersion wavelength in a 1.3-μm wavelength band and exhibits, in the 1.55-μm wavelength band, a positive chromatic dispersion and a positive dispersion slope. On the other hand, the dispersion-compensating optical fiber (hereinafter referred to as DCF) exhibits, in the 1.55-μm wavelength band, a negative chromatic dispersion and a negative dispersion slope. Hence, the respective lengths of the SMF and DCF are appropriately adjusted, so as to lower the dispersion slope of the optical transmission line as a whole. Also, since the SMF having a relatively large effective area is disposed on the upstream side in the signal propagating direction, the effective area of the whole transmission line is enhanced, and the nonlinearity of the optical transmission line is suppressed.

For example, the conventional optical transmission line disclosed in T. Naito, et. al, “1 Terabit/s WDM Transmission over 10,000 km,” ECOC′ 99, PD-2-1 (1999), hereinafter referred to as first conventional technique, comprises a configuration in which an SMF and a DCF are connected to each other. The conventional optical transmission line disclosed in Chikutani, et al., “Low Nonlinear PSCF+DCF Complex Transmission Line having Low Dispersion Slope and Low Nonlinearity,” IEICE Technical Report, OCS99-97, pp. 67-72 (1999), hereinafter referred to as second conventional example, comprises a configuration in which an SMF (hereinafter referred to as A_(eff)-enlarged PSCF) exhibiting an effective area A_(eff) greater than a commonly known value thereof and having a core region made of pure silica (non-intentionally doped silica), and a DCF are connected to each other. The conventional optical transmission line disclosed in M. Murakami, et al., “Quarter Terabit (25×10Gb/s) over 9288 km WDM Transmission Experiment Using Nonlinear Supported RZ Pulse in Higher Order Fiber Dispersion Managed Line,” ECOC′ 98, PD, pp. 79-81 (1998), hereinafter referred to as third conventional example, comprises a configuration in which an SMF (hereinafter referred to as Ge-SM) having a core region doped with Ge and a DCF are connected to each other.

The conventional optical transmission line disclosed in K. Fukuchi, et al., “1.1-Tb/s (55×20-Gb/s) Dense WDM Soliton Transmission Over 3,020-km Widely-Dispersion-Managed Transmission Line Employing 1.55/1.58-μm Hybrid Repeaters,” ECOC′ 99, PD-2-10 (1999), hereinafter referred to as fourth conventional example, comprises a configuration in which an SMF (hereinafter referred to as PSCF (Pure Silica Core Fiber)) having a core region made of pure silica and a DCF are connected to each other. The conventional optical transmission line disclosed in T. Tsuritani, et al., “1 Tbit/s (100×10.7 Gbit/s) Transoceanic Transmission Using 30 nm-Wide Broadband Optical Repeaters with A_(eff)-Enlarged Positive Dispersion Fibre and Slope-Compensating DCF,” ECOC′ 99, PD-2-7 (1999), hereinafter referred to as fifth conventional example, comprises a configuration in which an A_(eff)-Enlarged PSCF and a DCF are connected to each other.

SUMMARY OF THE INVENTION

The inventors studied the above-mentioned optical transmission lines according to the first to fifth conventional examples and, as a result, have found the following problems. Namely, effects of fully lowering the nonlinearity and dispersion slope may not be obtained in the optical transmission lines according to the first and second conventional examples since their bending loss is about 1 dB/m so that they are designed to become excessively resistant to bending. In the optical transmission lines according to the third and fourth conventional examples, the effect of lowering the nonlinearity may not fully be obtained since the relative refractive index difference of the core region in the DCF is assumed to be about 1.2%. The effect of fully lowering the nonlinearity may not be expected in the optical transmission line according to the fifth conventional example, since the relative refractive index difference of the core region in the DCF is assumed to be about 2.0%. Here, none of the optical transmission lines according to the third to fifth conventional examples is optimized in terms of the ratio of length of DCF in the whole optical transmission line, and the like.

In order to overcome the problems mentioned above, it is an object of the present invention to provide an optical transmission line comprising a structure for effectively lowering both the nonlinearity and dispersion slope, and an optical transmission system including the same.

The optical transmission line according to the present invention is a repeatered transmission line which has a predetermined span length of L and is disposed between stations, such as transmitting stations, repeater stations, and receiving stations, as a transmission medium suitable for WDM optical transmission utilizing signals of a plurality of channels different from each other. This optical transmission line comprises a single-mode optical fiber having a zero-dispersion wavelength in a 1.3-μm wavelength band, and a dispersion-compensating optical fiber for compensating for a chromatic dispersion of the single-mode optical fiber. The single-mode optical fiber and the dispersion-compensating optical fiber are successively disposed in this order along a signal propagating direction and are fusion-spliced to each other. The optical transmission line as a whole has an average dispersion slope S_(ave) of −0.0113 ps/nm²/km or more but 0.0256 ps/nm²/km or less at a wavelength of 1550 nm, and an equivalent effective area EA_(eff) of 50 μm² or more at the wavelength of 1550 nm.

In particular, the above-mentioned average dispersion slope S_(ave) and equivalent effective area EA_(eff) in the optical transmission line according to the present invention satisfy the following relationship:

f(S _(ave))≦EA _(eff) ≦g(S _(ave))  (1)

where f (S_(ave)) is a lower limit function which yields the lower limit of EA_(eff) by the expression:

942×S _(ave)+0.609×L+45.7

while using the average dispersion slope S_(ave) and the span length L as variable, and g(S_(ave)) is an upper limit function which yields the upper limit of EA_(eff) by the expression:

885×S _(ave)+0.609×L+60.7

while using the average dispersion slope S_(ave) and the span length L as variable.

The relationship represented by the above-mentioned expression (1) indicates an appropriate range of equivalent effective area EA_(eff) for controlling the bending loss within the range from 2 dB/m to 10 dB/m as a permissible range at a span length of 50 km in order to enable high-speed, large-capacity WDM optical transmission not only in C band (having a wavelength of 1530 to 1565 nm) but also in L band (having a wavelength of 1565 to 1625 nm).

Thus, this optical transmission line is a repeatered transmission line in which a single-mode optical fiber and a dispersion-compensating optical fiber are fusion-spliced to each other, in which signals successively propagate through the single-mode optical fiber and dispersion-compensating optical fiber in this order. At the wavelength of 1550 nm, the single-mode optical fiber and dispersion-compensating optical fiber have respective chromatic dispersions with polarities different from each other and respective dispersion slopes with polarities different from each other, whereby the absolute value of chromatic dispersion and the absolute value of dispersion slope become smaller in the optical transmission line as a whole. When the average dispersion slope S_(ave) and equivalent effective area EA_(eff) in the whole optical transmission line are set to satisfy the above-mentioned range, both the nonlinearity and average dispersion slope of the optical transmission line are lowered effectively, whereby a high bit rate (e.g., about 10 Gbits/s) of WDM transmission (high-speed, large-capacity optical transmission) is possible over a wider wavelength band, e.g., from 1530 nm to 1600 nm.

In addition, it is preferred that the optical transmission line as a whole have an average transmission loss of 0.185 dB/km or more but 0.210 dB/km or less at the wavelength of 1550 nm. Preferably, in the wavelength band from 1530 nm to 1600 nm, the average transmission loss is 0.185 dB/km or more but 0.220 dB/km or less. In each case, the transmission loss of the optical transmission line is sufficiently small, so that the input signal power can be made lower, whereby signal waveforms can effectively be restrained from deteriorating due to nonlinear effects.

In the single-mode optical fiber, the effective area A_(eff) at the wavelength of 1550 nm is preferably 100 μm² or more. While the signal power density decreases as the effective area increases, signal waveforms are restrained from deteriorating due to nonlinear effects, whereby the equivalent effective area EA_(eff) becomes greater. Preferably, the single-mode optical fiber has a core region made of pure silica not doped with GeO₂. This is because of the fact that, since the transmission loss caused by Rayleigh scattering is lower in the core region (the transmission loss of the whole optical transmission line is lower), the input signal power can be suppressed, whereby the equivalent effective area EA_(eff) becomes greater.

Preferably, the optical transmission line according to the present invention as a whole has a negative average chromatic dispersion at the wavelength of 1550 nm. This is because of the fact that the unstableness in modulation can be suppressed, whereby signal waveforms can effectively be restrained from deteriorating due to cross-phase modulation.

The optical transmission system according to the present invention is suitable for a WDM optical transmission system for enabling large-capacity optical communications and comprises, at least, a receiving station and a transmitting station. One or more repeater stations may be disposed between the receiving station and the transmitting station. The optical transmission line comprising the above-mentioned structure according to the present invention is employed as a repeatered transmission line disposed between the above-mentioned stations in at least one of repeatered transmission lines between a receiving station and a repeater station, between repeater stations, and between a repeater station and a receiving station. When no repeater station exists between a transmitting station and a receiving station, the above-mentioned optical transmission line according to the present invention can be employed as an entire transmission line from the transmitting station to the receiving station.

Since the absolute value of chromatic dispersion and the absolute value of dispersion slope in the whole optical transmission line are set smaller, and both the nonlinearity and average dispersion slope of the optical transmission line are lowered, a high bit rate (10 Gbits/s) of WDM transmission is possible over a wide wavelength band, e.g., from 1530 nm to 1600 nm.

The optical transmission system according to the present invention may also be configured such that the optical transmission line having the above-mentioned structure (exhibiting a negative chromatic dispersion at the wavelength of 1550 nm) is employed in each of a plurality of repeatered transmission lines continuous to each other by way of repeater stations and the like, whereas an optical transmission line constituted by a single-mode optical fiber alone is employed in a repeatered transmission line subsequent thereto. In this case, the absolute value of the average chromatic dispersion in the whole optical transmission system can be made smaller, whereby signal waveforms can effectively be restrained from deteriorating due to cumulative chromatic dispersion.

In typical optical transmission systems, an EDFA (Erbium-Doped Fiber Amplifier) is often utilized as an optical amplifier installed in each repeater station. However, the optical transmission line according to the present invention can elongate the repeating distance by utilizing a Raman amplifier as an optical amplifier.

The optical transmission line according to the present invention, in particular, can suppress the nonlinearity by elongating the span length (repeating distance) between stations, since it comprises a single-mode optical fiber having a zero-dispersion wavelength in the 1.3-μm wavelength band and a dispersion-compensating optical fiber for compensating for the chromatic dispersion of the single-mode optical fiber. Also, the span length, which has been about 50 km in typical submarine cables, can be elongated to 80 km or more by employing a Raman amplifier as an optical amplifier installed in a repeater station.

The present invention will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only, and thus are not to be considered as limiting the present invention.

Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a table showing the chromatic dispersion, dispersion slope, transmission loss, mode field diameter, effective area, and bending loss at a diameter of 20 mm in each of three kinds of DCFs (DCF1 to DCF3) at a wavelength of 1550 nm;

FIG. 2 is a graph showing the wavelength dependence of transmission loss of DCF1 in each of the respective states where it is wound about a bobbin and formed into a cable;

FIG. 3 is a graph showing the wavelength dependence of transmission loss of DCF2 in each of the respective states where it is wound about a bobbin and formed into a cable;

FIG. 4 is a graph showing the wavelength dependence of transmission loss of DCF3 in each of the respective states where it is wound about a bobbin and formed into a cable;

FIG. 5 is a diagram showing the configuration of an embodiment of the optical transmission line according to the present invention;

FIGS. 6A and 6B are views showing the cross-sectional structure of a DCF applicable to the optical transmission line according to the present invention and its refractive index profile, respectively;

FIG. 7 is a table showing characteristics of an SMF at a wavelength of 1550 nm;

FIG. 8 is a graph showing relationships between the DCF ratio and equivalent effective area EA_(eff) when the bending loss is 2 dB/m;

FIG. 9 is a graph showing relationships between the DCF ratio and equivalent effective area EA_(eff) when the bending loss is 10 dB/m;

FIG. 10 is a graph showing relationships between the average dispersion slope S_(ave) and maximum equivalent effective area EA_(eff) in the optical transmission line according to the present invention;

FIG. 11 is a diagram showing the configuration of an embodiment of the optical transmission system according to the present invention (in which each of nine continuous sections is provided with an optical transmission line constituted by an SMF and a DCF which are fusion-spliced to each other, whereas one section subsequent thereto is provided with an optical transmission line constituted by the SMF alone);

FIG. 12 is a graph hatching a range satisfying a condition concerning the average dispersion slope S_(ave) and equivalent effective area EA_(eff) in the graph shown in FIG. 10;

FIG. 13 is a table showing characteristics at a wavelength of 1550 nm of first to sixteenth samples (optical transmission lines) indicated by points (1) to (16) in the graph of FIG. 12;

FIG. 14 is a table showing characteristics of each of the first to sixth samples of optical transmission line at a wavelength of 1550 nm when the bending loss of DCF and the average dispersion slope S_(ave) of the whole transmission line are fixed at 2 dB/m and −0.004 ps/nm²/km, respectively;

FIG. 15 is a table showing characteristics of each of the seventh to twelfth samples of optical transmission line at a wavelength of 1550 nm when the bending loss of DCF and the average dispersion slope S_(ave) of the whole transmission line are fixed at 10 dB/m and −0.006 ps/nm²/km, respectively;

FIG. 16 is a table showing characteristics of each of the thirteenth to eighteenth samples of optical transmission line when the bending loss of DCF and the average dispersion slope S_(ave) of the whole transmission line are fixed at 2 dB/m and 0.020 ps/nm²/km, respectively;

FIG. 17 is a table showing characteristics of each of the nineteenth to twenty-fourth samples of optical transmission line at a wavelength of 1550 nm when the bending loss of DCF and the average dispersion slope S_(ave) of the whole transmission line are fixed at 10 dB/m and 0.020 ps/nm²/km, respectively;

FIG. 18 is a graph showing the wavelength dependence of transmission loss of an optical transmission line in which an A_(eff)-enlarged PSCF and a DCF are fusion-spliced to each other;

FIG. 19 is a table showing characteristics of each of the A_(eff)-enlarged PSCF and the DCF at a wavelength of 1550 nm;

FIG. 20 is a table showing characteristics at a wavelength of 1550 nm of the optical transmission line in which the A_(eff)-enlarged PSCF and the DCF are fusion-spliced to each other;

FIG. 21 is a table showing the transmission loss in which the A_(eff)-enlarged PSCF and the DCF are fusion-spliced to each other at each of wavelengths included within the wavelength range from 1530 nm to 1600 nm;

FIG. 22 is a table showing characteristics at a wavelength of 1550 nm of optical transmission lines in which other kinds of optical fibers are employed as the SMF of the optical transmission line according to the present invention;

FIG. 23 is a graph showing the relationship between span length (km) and equivalent effective area EA_(eff);

FIGS. 24A and 24B are graphs showing the power attenuation and phase shift amount versus signal propagation length in various samples (optical transmission lines) having a span length of 50 km with no Raman amplifiers, respectively;

FIGS. 25A and 25B are graphs showing the power attenuation and phase shift amount versus signal propagation length in various samples (optical transmission lines) having a span length of 80 km with no Raman amplifiers, respectively;

FIGS. 26A and 26B are graphs showing the power attenuation and phase shift amount versus signal propagation length in various samples (optical transmission lines) having a span length of 100 km with no Raman amplifiers, respectively;

FIG. 27 is a table showing characteristics of various optical fiber samples prepared for yielding the results of measurement shown in FIGS. 24A to 26B;

FIG. 28 is a graph showing the relationship between the contribution ratio of DCF to the nonlinearity index Δφ and the relative refractive index difference Δ⁺ of the DCF in each of the optical transmission lines having respective span lengths of 50 km, 80 km, and 100 km;

FIGS. 29A to 29C are graphs showing the relationships between Δφ relative value and Δ⁺ of DCF at each standard in the optical transmission lines having respective span lengths of 50 km, 80km, and 100 km when the gain by Raman amplification is fixed; and

FIG. 30 is a table showing characteristics at a wavelength of 1550 nm of an A_(eff)-enlarged PSCF employed as the SMF of each of thirty-first to forty-sixth samples of samples of the optical transmission line according to the present invention;

FIG. 31 is a table showing characteristics at a wavelength of 1550 nm of samples (DCF10-DCF25) of a dispersion compensating Fiber employed to of the optical transmission line according to the present invention;

FIG. 32 is a table showing characteristics at a wavelength of 1550 nm of each of thirty-first to forty-sixth samples of the optical transmission line according to the present invention;

FIG. 33 is a graph showing relationships between the average dispersion slope S_(ave) and equivalent effective area EA_(eff) in thirty-first to forty-sixth samples of the optical transmission line according to the present invention; and

FIG. 34 is a graph showing the relationship between span length (km) and equivalent effective area EA_(eff), regarding to thirty-first to forty-sixth samples of the optical transmission line according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following, embodiments of the optical transmission line according to the present invention and the optical transmission system including the same will be explained in detail with reference to FIGS. 1 to 5, 6A, 6B, 7 to 23, 24A to 26B, 27, 28, 29A to 29C and 30 to 34. In the explanation of drawings, constituents identical to each other will be referred to with numerals or letters identical to each other without repeating their overlapping descriptions.

First, for each of three kinds of DCFs having the characteristics (at a wavelength of 1550 nm) shown in FIG. 1, the inventors measured respective transmission loss characteristics in the state where it was wound about a plastic bobbin (having a diameter of 280 mm) and where it was formed into a cable (assuming a submarine cable). As a result, the transmission of DCF has been found to become lower in the state formed into a cable than in the state wound about the bobbin.

FIG. 1 is a table showing the chromatic dispersion, dispersion slope, transmission loss, mode field diameter (MFD), effective area (A_(eff)), and bending loss at a diameter of 20 mm (measured in the state wound about a mandrel having a diameter of 20 mm) in each of the three kinds of DCFs (DCF1, DCF2, and DCF3) at the wavelength of 1550 nm. FIGS. 2 to 4 are graphs showing the wavelength dependence characteristics of transmission loss in DCF1, DCF2, and DCF3, respectively. In FIGS. 2 to 4, curves G210, G310, and G410 show the respective transmission loss characteristics of DCFs in the state wound about the bobbin, whereas curves G220, G320, and G420 show the respective transmission loss characteristics of DCFs in the state formed into a cable.

The following facts can be seen from the graphs shown in FIGS. 2 to 4. Namely, when compared with the state wound about the bobbin, the DCF in the cable form yields a lower bending loss, and a lower transmission loss on the longer wavelength side, thereby widening the permissible range of bending level. If the bending loss is about 2 dB/m, the DCF will not increase the loss until the wavelength reaches about 1625 nm even in the state wound about the bobbin, which is preferable for transmitting signals of L band (having a wavelength of 1565 to 1625 nm). If the bending loss is about 10 dB/m, on the other hand, the DCF will not increase the loss until the wavelength reaches about 1625 nm when formed into a cable, which is preferable for transmitting signals of L band. If the bending loss is about 50 dB/m, the DCF will not increase the loss until the wavelength reaches about 1565 nm when formed into a cable, which is preferable for transmitting signals of C band (having a wavelength of 1530 to 1565 nm). Thus, the permissible range of bending loss in DCF has been determined from the characteristics after being formed into a cable. Therefore, the inventors studied the dependence of the relationship between the equivalent effective area and dispersion slope upon bending loss, and then the optimization of the relationship between the equivalent effective area and dispersion slope from the permissive range of bending loss determined as mentioned above.

Here, the equivalent effective area EA_(eff) of an optical transmission line is defined as follows. First, as an amount quantitatively representing the nonlinearity, a value Δφ (nonlinearity index) obtained when the phase shift amount caused by self-phase modulation is integrated over the repeating section (span length L) is introduced. This Δφ is given by the following expressions (2a) and (2b): $\begin{matrix} {{\Delta \quad \varphi} = {k{\int_{0}^{L}{\frac{N_{2}(z)}{A_{eff}(z)}{P(z)}\quad {z}}}}} & \left( {2a} \right) \end{matrix}$

 P(z)=P ₀exp(−α·z)  (2b)

where k is the wave number, z is the variable representing the distance (position in the longitudinal direction) from the light input end of the optical transmission line, N₂(z) is the nonlinear refractive index (according to XPM (cross-phase modulation) method) of the optical transmission line at the position z, A_(eff)(z) is the effective area of the optical transmission line at the position z, P(z) is the optical power at the position z of optical transmission line, a is the transmission loss of the optical transmission line, and P₀ is the optical power at the light input end of the optical transmission line, which is adjusted such that the optical power P(L) at the output end of the line becomes constant in order to attain a predetermined S/N ratio at the output end of the line.

Also assumed is a non-zero dispersion-shifted optical fiber (hereinafter referred to as DSF) having a transmission loss of 0.210 dB/km, a nonlinear refractive index N₂ of 3.2×10⁻²⁰ m²/W, and an effective area A_(eff) of 55 μm² as characteristics at the wavelength of 1550 nm, and a length L. When the nonlinearity index Δφ_((DSF)) of the DSF having an effective area A_(eff) is equal to the Δφ of the optical transmission line, this effective area A_(eff) is defined as the equivalent effective area EA_(eff) of the optical transmission line. Using these parameters, the equivalent effective area of the optical transmission line EA_(eff) is represented by the following expression (3): $\begin{matrix} {{EA}_{eff} = {A_{{eff}{({DSF})}}\frac{\Delta \quad \varphi_{({DSF})}}{\Delta \quad \varphi}}} & (3) \end{matrix}$

FIG. 5 is a diagram showing the configuration of an optical transmission line according to the present invention. As depicted, this optical transmission line 1 is disposed as a repeatered transmission line between a station (transmitting station or repeater station) 2 and a station (receiving station or repeater station) 2. The optical transmission line 1 comprises a configuration in which an SMF 11 on the upstream side and a DCF 12 on the downstream side are fusion-spliced to each other. The SMF 11 is a single-mode optical fiber having a zero-dispersion wavelength in the 1.3-μm wavelength band and a positive chromatic dispersion and a positive dispersion slope in the 1.55-μm wavelength band. The DCF 12 is a dispersion-compensating optical fiber having a negative chromatic dispersion and a negative dispersion slope in the 1.55-μm wavelength band. When the station 2 is a repeater station, this station is provided with an EDFA or Raman amplifier as an optical amplifier 20.

FIG. 6A is a view showing the cross-sectional structure of the DCF 12. The DCF 12 comprises a core region 12 a having a refractive index n, and extending along a predetermined axis, e.g., an optical axis; an inner cladding region 12 b, disposed at the outer periphery of the core region 12 a, having a refractive index n₂ lower than that of the core region 12 a; and an outer cladding region 12 c, disposed at the outer periphery of the inner cladding region 12 b, having a refractive index n₃ higher than that of the inner cladding region 12 b. Also, the coreregion 12 a has an outside diameter 2 a and a relative refractive index difference of Δ⁺ (=(n₁ ²−n₃ ²)/2n₃ ²) with respect to the outer cladding region 12 cacting as a reference region, whereas the inner cladding region 12 b has an outside diameter 2 b and a relative refractive index difference of Δ⁻ (=(n₃ ²−n₂ ²)/2n₃ ²) with respect to the outer cladding region 12 c acting as the reference region. Here, the ratio of the outside diameter of the core region 12 a to the outside diameter of the inner cladding region 12 b is expressed by Ra (=a/b).

The refractive index profile 120 shown in FIG. 6B corresponds to the refractive index of each part on the line L in FIG. 6A, whereas areas 121, 122, and 123 indicate the refractive indices of core regions 12 a, inner cladding region 12 b, and outer cladding region 12 c on the line L in FIG. 6A, respectively.

The inventors carried out studies about optimal designing of the optical transmission line 1 by changing the outside diameter 2 a, relative refractive index difference Δ⁺, and outside diameter ratio Ra of the core region 12 a of the DCF 12 while fixing the relative refractive index difference Δ⁻ of the inner cladding region 12 b of the DCF 12 at −0.4%. Further, while fixing the bending loss of DCF 12 (at the wavelength of 1550 nm and a bending diameter of 20 mm) at a predetermined value and changing the relative refractive index difference Δ⁺ of the core region of DCF 12 within the range from 1.0% to 2.0%, the chromatic dispersion, dispersion slope, and effective area A_(eff) of the DCF 12 were calculated, whereby the equivalent effective area EA_(eff) of the optical transmission line 1 with respect to each value of refractive index difference Δ⁺ of the DCF 12 was determined.

FIG. 7 is a table showing characteristics of the SMF 11 at the wavelength of 1550 nm. The SMF 11 has a core region made of pure silica (non-intentionally doped silica) and exhibits a transmission loss of 0.170 dB/km, an effective area A_(eff) of 110 μm², a chromatic dispersion of 20.4 ps/nm/km, a dispersion slope of 0.059 ps/nm²/km, and a nonlinear refractive index N₂ of 2.8×10⁻²⁰ m²/W. Namely, the SMF 11 is an A_(eff)-enlarged PSCF.

Under the condition where the length L of the optical transmission line 1 as the repeatered transmission line was 50 km and the average chromatic dispersion of the whole optical transmission line was −2 ps/nm/km, the inventors studied about the optimum length ratio between the SMF 11 and DCF 12. The average transmission loss of optical transmission line 1 is determined by a weighted average of the respective transmission losses of SMF 11 and DCF 12 with their lengths, whereas the average dispersion slope of optical transmission line 1 is determined by a weighted average of the respective dispersion slopes of SMF 11 and DCF 12 with their lengths. The equivalent effective area EA_(eff) of the optical transmission line 1 is obtained by carrying out the integrating calculations of the above-mentioned expressions (2a) and (2b) and utilizing the above-mentioned expression (3).

The average chromatic dispersion of optical transmission line 1 is set to −2 ps/nm/km due to the following reasons. In optical transmission lines employed in submarine cables, each repeatered transmission line is provided with a negative chromatic dispersion in general in order to prevent modulation instability. Therefore, providing the optical transmission line 1 with a negative average chromatic dispersion is preferable since it restrains the modulation instability. Such setting of the average chromatic dispersion is also effective in restraining signal waveforms from deteriorating due to cross-phase modulation (XPM). In view of the foregoing reasons, the average chromatic dispersion of the optical transmission line 1 is set to −2 ps/nm/km.

Under the above-mentioned conditions, the inventors determined a relationship between the length ratio of DCF 12 (hereinafter referred to as DCF ratio) in the optical transmission line 1 acting as a repeatered transmission line and the equivalent effective area EA_(eff) of the optical transmission line 1 when the bending loss (at the wavelength of 1550 nm and a bending diameter of 20 mm) was fixed at a given value within the range from 2 dB/m to 10 dB/m as a range of bending loss in which the loss would not increase until the wavelength reached 1600 nm in a state where the optical transmission line 1 was formed into a submarine cable.

FIG. 8 is a graph showing the relationship between the DCF ratio and equivalent effective area EA_(eff) when the bending loss is 2 dB/m at each value of the average dispersion slope S_(ave) of optical transmission line land the relative refractive index difference Δ⁺ of DCF 12. FIG. 9 is a graph showing the relationship between the DCF ratio and equivalent effective area EA_(eff) when the bending loss is 10 dB/m at each value of the average dispersion slope S_(ave) of optical transmission line 1 and the relative refractive index difference Δ⁺ of DCF 12. Here, curve G810 plots the results of calculation of DCF 12 concerning the average dispersion slope S_(ave) of −0.004 ps/nm²/km when the relative refractive index differenceΔ⁺ of DCF 12 is 1.0%, 1.2%, 1.4%, 1.6%, 1.8%, and 2.0%, respectively. Similarly, in FIGS. 8 and 9, curves G820, G830, G840, G910, G920, G930, and G940 indicate the respective results of calculation when the average dispersion slope S_(ave) is 0.000 ps/nm²/km, 0.010 ps/nm²/km, 0.020 ps/nm²/km, −0.006 ps/nm²/km, 0.000 ps/nm²/km, 0.010 ps/nm²/km, and 0.020 ps/nm²/km, respectively.

FIG. 10 is a graph showing relationships between the average dispersion slope S_(ave) in the optical transmission line 1 and the maximum value of equivalent effective area EA_(eff) when the average dispersion slope S_(ave) is obtained. In FIG. 10, curves G1010, G1020, G1030, G1040, and G1050 indicate the respective relationships when the bending loss (at the wavelength of 1550 nm and a bending loss of 20 mm) is 4 dB/m, 6 dB/m, 8 dB/m, and 10 dB/m.

The relationships between the average dispersion slope S_(ave) and equivalent effective area EA_(eff) (curves G1010 to G1050) shown in FIG. 10 are approximated by the following expression (4): $\begin{matrix} {{EA}_{eff} = {\frac{0.4481 + \sqrt{(0.4481)^{2} - {4 \times 0.00518 \times \left( {3.29 - {\ln \left\{ {S_{ave} + 0.0053 + {0.016\left\lbrack {{\log \quad 10({BL})} - {\log \quad 2}} \right\rbrack}} \right\}}} \right)}}}{2 \times 0.00518} + {12\left\lbrack {{\log ({BL})} - {\log \quad 2}} \right\rbrack}}} & (4) \end{matrix}$

where BL is the bending loss of DCF 12 at a bending diameter of 20 mm. Namely, each of curves G1010 to G1050 is represented by the above-mentioned expression (4) as a graph indicating the relationship between the average dispersion slope S_(ave)and the equivalent effective area EA_(eff).

When the optical transmission line is formed into a submarine cable, it is desirable that the bending loss be prevented from increasing in the range where the wavelength is not longer than 1625 nm, for which the bending loss BL of DCF 12 is required to be 10 dB/m or less. On the other hand, the bending loss BL of DCF 12 is preferably 2 dB/m or more since optical characteristics deteriorate in terms of transmission loss and nonlinearity when it is excessively resistant to bending (i.e., when its bending loss is extremely low).

When actually making a submarine cable, an optical transmission line having a negative average chromatic dispersion is employed in a plurality of repeatered transmission lines which are continuous to each other by way of repeaters, and an optical transmission line having a positive chromatic dispersion is employed in a repeatered transmission line subsequent thereto, so that the average chromatic dispersion of the whole submarine cable becomes substantially 0 ps/nm/km. Such a configuration effectively restrains signal waveforms from deteriorating due to the cumulative chromatic dispersion of the whole submarine cable.

FIG. 11 is a view showing the configuration of an optical transmission system according to the present invention. In this optical transmission system, a plurality of repeater stations 2 are disposed between a transmitting station 200 and a receiving station 300. In the optical transmission system shown in FIG. 11, the above-mentioned optical transmission line 1 in which the SMF 11 and DCF 12 are fusion-spliced to each other is employed as a repeatered transmission line in each of nine sections which are continuous to each other by way of the repeater stations 2, and an optical transmission line made of the SMF 11 alone is employed as the repeatered transmission line in one section subsequent thereto. The optical transmission line 1 (repeatered transmission line) in each of the nine sections has a length of 50 km and an average chromatic dispersion of −2 ps/nm/km. In order for the average chromatic dispersion of the 10 sections in total to become substantially 0 ps/nm/km, the section made of the SMF 11 alone is required to have an optical transmission line length of 44 km (=2 (ps/nm/km)×50 (km)×9/20.4 (ps/nm/km)), whereby the total length (of 10 sections) of the optical transmission system becomes 494 km (=50×9+44).

In the signal transmission at 10 Gbits/s, it is considered necessary to suppress the absolute value of cumulative chromatic dispersion in optical transmission lines to 1000 ps/nm or less in general. When the signal wavelength band includes both C and L bands (i.e., when the signal wavelength band ranges from 1530 nm to 1600 nm with a bandwidth of 70 nm), the 10 sections in total shown in FIG. 11 are required to have an average dispersion slope of 0.0286 ps/nm²/km (=1000 (ps/nm) /500 (km) /70 (nm) ) or less in order to fulfill the signal transmission at 10 Gbits/s. In the signal transmission at 20 Gbits/s, it is considered necessary to suppress the absolute value of cumulative chromatic dispersion in optical transmission lines to 250 ps/nm or less in general, whereby the 10 sections in total shown in FIG. 11 are required to have an average dispersion slope of 0.0072 ps/nm²/km or less in order to fulfill the signal transmission at 20 Gbits/s when the signal wavelength band includes both C and L bands. On the other hand, the average dispersion slope of the 10 sections shown in FIG. 11 is preferably −0.005 ps/nm²/km or more in order to prevent excess compensation from occurring.

In view of the foregoing, the average dispersion slope of the 10 sections in total shown in FIG. 11 is preferably −0.005 ps/nm²/km or more but 0.0286 ps/nm²/km or less, more preferably −0.005 ps/nm²/km or more but 0.0072 ps/nm²/km or less. Consequently, the average dispersion slope S_(ave) of the optical transmission line 1 employed in each of the nine sections other than the repeating section made of the SMF 11 alone is preferably −0.0113 ps/nm² /km or more but 0.0256 ps/nm²/km or less, more preferably −0.0113 ps/nm²/km or more but 0.0021 ps/nm²/km or less.

In addition to the foregoing conditions, the equivalent effective area EA_(eff) is set to 50 μm² or greater, whereby the nonlinearity of the optical transmission line 1 is effectively lowered. Further, in view of the fact that the permissible range of bending loss (at the wavelength of 1550 nm and a bending diameter of 20 mm) is set so as to become 2 dB/m or more but 10 dB/m or less in the optical transmission line 1 having a span length of 50 km, the above-mentioned average dispersion slope S_(ave) and equivalent effective area EA_(eff) preferably satisfy the relationship of:

f(S_(ave))≦EA _(eff) ≦g(S _(ave))  (5)

where f(S_(ave)) is a lower limit function which yields the lower limit of EA_(eff) by the expression: $\frac{0.4481 + \sqrt{(0.4481)^{2} - {4 \times 0.00518 \times \left\lbrack {3.29 - {\ln \left( {S_{ave} + 0.0053} \right)}} \right\rbrack}}}{2 \times 0.00518}$

while using S_(ave) as a variable, and g(S_(ave)) is an upper limit function which yields the upper limit of EA_(eff) by the expression: $\frac{0.4481 + \sqrt{(0.4481)^{2} - {4 \times 0.00518 \times \left\{ {3.29 - {\ln \left\lbrack {S_{ave} + 0.0053 + {0.016\left( {{\log \quad 10} - {\log \quad 2}} \right)}} \right\rbrack}} \right\}}}}{2 \times 0.00518} + {12\left( {{\log \quad 10} - {\log \quad 2}} \right)}$

while using S_(ave) as a variable.

When the condition of the above-mentioned expression (5) is satisfied, both the nonlinearity and dispersion slope of the optical transmission line 1 are effectively lowered. Therefore, this optical transmission line 1 and an optical transmission system using the same enable high-speed, large-capacity WDM transmissions at 10 Gbit/s.

FIG. 12 is a graph hatching a range satisfying the condition given by the above-mentioned expression (5) (the relationship between the average dispersion slope S_(ave) and equivalent effective area EA_(eff)) in the graph shown in FIG. 10. Here, curves G1210, G1220, G1230, G1240, and G1250 in FIG. 12 correspond to curves G1010, G1020, G1030, G1040, and G1050 in FIG. 10, respectively. FIG. 13 is a table showing characteristics at each of points (1) to (16) plotted in FIG. 12. For each of points (1) to (16), FIG. 13 shows, successively from the left side, the DCF ratio (%) of optical transmission line 1, the average dispersion slope S_(ave) (ps/nm²/km) of optical transmission line 1, the span loss (dB/m) of optical transmission line 1, the equivalent effective area EA_(eff) (dm²) of optical transmission line 1, the relative refractive index difference Δ⁺ (%) of core region 12 a of DCF 12, the outside diameter ratio Ra of DCF 12, the outside diameter 2 b (μm) of inner cladding region 12 b of DCF 12, the transmission loss α (dB/km) of DCF 12, the chromatic dispersion (ps/nm/km) of DCF 12, the effective area A_(eff) (dm²) of DCF 12, the bending loss (dB/m) of DCF 12 at a diameter of 20 mm, the length L_(SMF) (km) of SMF 11, the length L_(DCF) (km) of DCF 12, and the nonlinear refractive index N₂ (×10⁻²⁰ m²/W) of DCF 12.

The dispersion slope of optical transmission line 1 is further reduced in particular when the average dispersion slope S_(ave) of optical transmission line 1 is −0.0113 ps/nm²/km or more but 0.0021 ps/nm²/km or less. Hence, the optical transmission line 1 and an optical transmission system including the same enable high-speed, large-capacity WDM transmissions at 20 Gbits/s. The nonlinearity of optical transmission line 1 is further lowered when the equivalent effective area EA_(eff) is 55 μm² or more, more preferably 60 μm² or more.

FIG. 14 is a table showing characteristics at the wavelength of 1550 nm of each of first to sixth samples of optical transmission line 1 when the bending loss of DCF 12 and the average dispersion slope S_(ave) of the whole transmission line are fixed at 2 dB/m and −0.004 ps/nm²/km, respectively. The first to sixth samples have respective DCFs 12 with structures different from each other. FIG. 15 is a table showing characteristics at the wavelength of 1550 nm of each of seventh to twelfth samples of optical transmission line 1 when the bending loss of DCF 12 and the average dispersion slope S_(ave) of the whole transmission line are fixed at 10 dB/m and −0.006 ps/nm²/km, respectively. The seventh to twelfth samples have respective DCFs 12 with structures different from each other. FIG. 16 is a table showing characteristics at the wavelength of 1550 nm of each of thirteenth to eighteenth samples of optical transmission line 1 when the bending loss of DCF 12 and the average dispersion slope S_(ave) of the whole transmission line are fixed at 2 dB/m and 0.020 ps/nm²/km, respectively. The thirteenth to eighteenth samples have respective DCFs 12 with structures different from each other. FIG. 17 is a table showing characteristics at the wavelength of 1550 nm of each of nineteenth to twenty-fourth samples of optical transmission line 1 when the bending loss of DCF 12 and the average dispersion slope S_(ave) of the whole transmission line are fixed at 10 dB/m and 0.020 ps/nm²/km, respectively. The nineteenth to twenty-fourth samples have respective DCFs 12 with structures different from each other.

Each of FIGS. 14 to 17 shows, successively from the left side, the relative refractive index difference Δ⁺ (%) of core region of DCF 12, the outside diameter ratio Ra of DCF 12, the outside diameter 2b (μm) of inner cladding region 12 b of DCF 12, the transmission loss α (dB/km) of DCF 12, the chromatic dispersion (ps/nm/km) of DCF 12, the dispersion slope (ps/nm²/km) of DCF 12, the effective area A_(eff) (μm²) of DCF 12, the nonlinear refractive index N₂ (×10⁻²⁰ m²/W), the DCF ratio (%) of each sample (optical transmission line 1), the equivalent effective area A_(eff) (μm²) of optical transmission line 1, and the difference in equivalent effective area EA_(eff). The difference in equivalent effective area EA_(eff) represents the difference between the maximum value of equivalent effective area EA_(eff) (maximum equivalent effective area) that can be realized under each condition and the equivalent effective area EA_(eff) at each relative refractive index difference Δ⁺.

From the tables of FIGS. 14 to 17, it can be seen that, when the bending loss of DCF 12 is 2 dB/m, the relative refractive index difference Δ⁺ (%) at which the equivalent effective area EA_(eff) becomes 95% or more of the maximum equivalent effective area is 1.4% or more but 1.8% or less. When the relative refractive index difference Δ⁺ (%) of core region 12 a of DCF 12 falls within this range, the optical transmission line 1 can substantially attain the maximum equivalent effective area EA_(eff), thus becoming an optimal design. Also, the above-mentioned range of equivalent effective area EA_(eff) can be expressed as a DCF ratio of 23% or more but 36% or less. If the average chromatic dispersion of optical transmission line 1 is −3 ps/nm/km or more but 0 ps/nm/km or less, the chromatic dispersion of DCF 12 will be at −81 ps/nm/km or more but −36 ps/nm/km or less.

As in the foregoing, when an appropriate range of value is set for each of the DCF ratio and average chromatic dispersion slope S_(ave) of optical transmission line 1 and the bending loss of DCF 12, the equivalent effective area EA_(eff) of optical transmission line can be made greater than that of conventional optical transmission lines, whereby the nonlinearity of optical transmission line 1 is lowered more effectively.

Also, the transmission loss of the whole optical transmission line 1 at the wavelength of 1550 nm is 0.185 dB/km or more but 0.210 dB/km or less, thus being equal to or less than the transmission loss of DSF. When there is no loss caused by bending, the loss caused by Rayleigh scattering in the optical transmission line 1 becomes the greatest at the wavelength of 1530 nm within the wavelength band from 1530 nm to 1600 nm. Since the difference in loss is about 0.01 dB/km, the actual transmission loss in this wavelength band becomes 0.185 dB/km or more but 0.220 dB/km or less. As a consequence, signals can be fed into the SMF 11 at a lower power, whereby the optical transmission line 1 effectively restrains nonlinear optical phenomena from occurring.

A specific configuration of the optical transmission line 1 according to the present invention will now be explained with reference to FIGS. 18 to 21. FIG. 18 is a graph showing the wavelength dependence of transmission loss of an optical transmission line having a configuration in which an A_(eff)-enlarged PSCF and a DCF are fusion-spliced to each other. FIG. 19 is a table showing characteristics of each of the A_(eff)-enlarged PSCF and the DCF at the wavelength of 1550 nm. FIG. 20 is a table showing characteristics at the wavelength of 1550 nm of the optical transmission line having the configuration in which the A_(eff)-enlarged PSCF and the DCF are fusion-spliced to each other. FIG. 21 is a table showing the transmission loss of the optical transmission line having the configuration in which the A_(eff)-enlarged PSCF and the DCF are fusion-spliced to each other at each of wavelengths included within the wavelength band from 1530 nm to 1600 nm. Here, the loss between the A_(eff)-enlarged PSCF and the DCF upon fusion-splicing is 0.11 dB.

As characteristics at the wavelength of 1550 nm, the A_(eff)-enlarged PSCF has a transmission loss of 0.171 dB/km, a chromatic dispersion of 20.4 ps/nm/km, a dispersion slope of 0.059 ps/nm²/km, an effective area A_(eff) of 110.0 μm², and a nonlinear refractive index N₂ of 2.8×10⁻²⁰ m²/W. As characteristics at the wavelength of 1550 nm, the DCF has a transmission loss of 0.243 dB/km, a chromatic dispersion of −48.6 ps/nm/km, a dispersion slope of −0.128 ps/nm²/km, an effective area A_(eff) of 20.7 μm², and a nonlinear refractive index N₂ of 3.85×10⁻²⁰ m²/W.

The optical transmission line having a configuration in which the A_(eff)-enlarged PSCF and DCF having the above-mentioned characteristics are fusion-spliced to each other, as a whole, has an average transmission loss of 0.197 dB/km, an average chromatic dispersion of −2 ps/nm/km, an average dispersion slope of −0.0017 ps/nm²/km, and an equivalent effective area EA_(eff) of 71.4 m². In the wavelength band from 1530 nm to 1600 nm, the optical transmission line has an average transmission loss of 0.195 dB/km or more but 0.203 dB/km or less, which is substantially uniform.

At the wavelength of 1550 nm, the above-mentioned optical transmission line has a transmission loss of 0.185 dB/km or more but 0.210 dB/km or less, which is equal to or less than the transmission loss of DSF. In the wavelength band from 1530 nm to 1600 nm, the optical transmission line exhibits an average transmission loss of 0.185 dB/nm or more but 0.220 dB/km or less. Therefore, signals can be fed into the A_(eff)-enlarged PSCF at a lower power, whereby the optical transmission line can effectively restrain nonlinear optical phenomena from occurring.

Though the foregoing explanation relates to a case where the SMF 11 of optical transmission line 1 is an A_(eff)-enlarged PSCF, the SMF 11 is not limited to the A_(eff)-enlarged PSCF. FIG. 22 is a table showing characteristics at the wavelength of 1550 nm in other optical transmission lines in which different kinds of optical fibers are employed as the SMF 11 of optical transmission line 1. This table shows the transmission loss (dB/km), chromatic dispersion (ps/nm/km), effective area A_(eff) (μm²), and nonlinear refractive index N₂ (×10⁻²⁰ m²/W) for each of a normal SMF whose core region is doped with Ge (Ge-SM), a normal SMF whose core region is made of pure silica (PSCF), a Ge-SM whose effective area is enlarged (A_(eff)-enlarged PSCF) and a Ge-SM whose effective area is enlarged (A_(eff)-enlarged Ge-SM) which are employed as the SMF 11, and the equivalent effective area EA_(eff) (μm² of the optical transmission line including the corresponding one of these SMFs. As the DCF 12, one having the characteristics corresponding to those of point (3) in FIG. 13 is employed.

As can be seen from FIG. 22, the equivalent effective area EA_(eff) of the SMFs whose core is made of pure silica (PSCF and A_(eff)-enlarged PSCF) is greater by about 10% than that of the SMFs whose core region is made of pure silica (Ge-SM and A_(eff)-enlarged Ge-SM). This is because of the fact that the PSCF and A_(eff)-enlarged PSCF yield a smaller transmission loss caused by Rayleigh scattering, so that the transmission loss of the whole transmission line is smaller, whereby the input signal power can be lowered. On the other hand, the equivalent effective area EA_(eff) of the SMFs whose effective area is enlarged (A_(eff)-enlarged Ge-SM and A_(eff)-enlarged PSCF) is also greater by about 10% than that of the normal SMFs whose effective area is not enlarged (Ge-SM and PSCF). This is because of the fact that the A_(eff)-enlarged Ge-SM and A_(eff)-enlarged PSCF have a greater effective area, so that the signal power density can be suppressed low, whereby signal waveforms can be restrained from deteriorating due to nonlinear effects. Hence, the equivalent effective area EA_(eff) of the A_(eff)-enlarged PSCF is greater by about 20% than that of the Ge-SM. Thus, the nonlinearity of optical transmission line is most effectively lowered when the A_(eff)-enlarged PSCF is employed as the SMF 11.

In typical optical transmission systems, EDFA is often utilized as an optical amplifier installed in each repeater station. However, it has recently been proposed to elongate the repeating distance by utilizing a Raman amplifier as an optical amplifier.

In particular, the optical transmission line 1 according to the present invention has a configuration in which the SMF 11 having a zero-dispersion wavelength in the 1.3-μm wavelength band and the DCF 12 for compensating for the chromatic dispersion of the SMF 11 are fusion-spliced to each other. Therefore, it can suppress the nonlinearity by elongating the span length between stations (repeating distance, i.e., the total length of the optical transmission line 1). Also, when distributed Raman amplification using a repeatered transmission line is employed, the span length, which has been about 50 km in a typical submarine cable, can be elongated to 80 km or more.

As shown in FIG. 23, the equivalent effective area EA_(eff)and the length of the optical transmission line 1 (span length) have such a relationship that the equivalent effective area EA_(eff) increases as the span length elongates. Therefore, it is seen that, as the span length increases, the equivalent effective area EA_(eff) becomes greater, and the relative nonlinearity lowers conversely. Here, FIG. 23 shows the results of calculation concerning a DCF whose core region 12 a has a relative refractive index difference Δ⁺ of 1.4%.

Since the curve shown in FIG. 23 appears to be substantially linear, the equivalent effective area EA_(eff) and span length L (km) in the optical transmission line 1 can be related to each other as defined by the following expression (6):

EA _(eff)=0.981·L+C(const)  (6)

If the span length L is 50 km here, then the constant C1 in the above-mentioned expression (6) when the equivalent effective area EA_(eff) is at the lower limit f(S_(ave)) is given by the expression of f(S_(ave))−0.981×50=f(S_(ave))−49.05, since the relationship of the above-mentioned expression (5) holds. On the other hand, the constant C2 in the above-mentioned expression (6) when the equivalent effective area EA_(eff) is at the upper limit g(S_(ave)) is given by the expression of g(S_(ave))−0.981×50=g(S_(ave))−49.05. Therefore, the optimal equivalent effective area EA_(eff) when the span length is L (km) preferably satisfies the following expression (7):

0.981·L+C1≦EA _(eff)≦0.981·L+C2  (7)

Satisfying the condition of expression (7) yields a repeatered transmission line in which the effective area EA_(eff) increases as the span length elongates, so as to effectively suppress the nonlinearity.

Also, the inventors calculated the power attenuation and phase shift amount versus signal transmission length in optical transmission lines in which no distributed Raman amplification is employed. FIGS. 24A and 24B are graphs showing the power attenuation and phase shift amount versus signal propagation length in various samples (optical transmission lines) having a span length of 50 km in which no Raman amplification is employed, respectively. FIGS. 25A and 25B are graphs showing the power attenuation and phase shift amount versus signal propagation length in various samples (optical transmission lines) having a span length of 80 km in which no Raman amplification is employed, respectively. FIGS. 26A and 26B are graphs showing the power attenuation and phase shift amount versus signal propagation length in various samples (optical transmission lines) having a span length of 100 km in which no Raman amplification is employed, respectively. In each of the cases with span lengths of 50 km, 80 km, and 100 km, the output power from the optical transmission line was fixed at −22 dBm, whereas an optical transmission line in which the SMF and DCF4 having the characteristics shown in FIG. 27 were fusion-spliced to each other, an optical transmission line in which the SMF and DCF5 having the characteristics shown in FIG. 27 were fusion-spliced to each other, an optical transmission line in which the SMF and DCF6 having the characteristics shown in FIG. 27 were fusion-spliced to each other, an optical transmission line in which the SMF and DCF7 having the characteristics shown in FIG. 27 were fusion-spliced to each other, an optical transmission line in which the SMF and DCF8 having the characteristics shown in FIG. 27 were fusion-spliced to each other, and an optical transmission line in which the SMF and DCF9 having the characteristics shown in FIG. 27 were fusion-spliced to each other were prepared as twenty-fifth, twenty-sixth, twenty-seventh, twenty-eighth, twenty-ninth, and thirtieth samples, respectively. In each of the twenty-fourth to thirtieth samples, the dispersion compensation ratio by DCF is 100%, and the bending loss at a bending diameter of 20 mm is 10 dB/m.

In FIGS. 24A and 24B, curves G2410 a and G2410 b, curves G2420 a and G2420 b, curves G2430 a and G2430 b, curves G2440 a and G2440 b, curves G2450 a and G2450 b, and curves G2460 a and G2460 b are those concerning the twenty-fifth, twenty-sixth, twenty-seventh, twenty-eighth, twenty-ninth, and thirtieth samples, respectively. In FIGS. 25A and 25B, curves G2510 a and G2510 b, curves G2520 a and G2520 b, curves G2530 a and G2530 b, curves G2540 a and G2540 b, curves G2550 a and G2550 b, and curves G2560 a and G2560 b are those concerning the twenty-fifth, twenty-sixth, twenty-seventh, twenty-eighth, twenty-ninth, and thirtieth samples, respectively. In FIGS. 26A and 26B, curves G2610 a and G2610 b, curves G2620 a and G2620 b, curves G2630 a and G2630 b, curves G2640 a and G2640 b, curves G2650 a and G2650 b, and curves G2660 a and G2660 b are those concerning the twenty-fifth, twenty-sixth, twenty-seventh, twenty-eighth, twenty-ninth, and thirtieth samples, respectively.

As shown in FIGS. 24B, 25B, and 26B in particular, the contribution of SMF becomes greater than that of DCF as the span length elongates. For making it easier to see this result, FIG. 28 shows the relationship between the contribution of DCF to the nonlinearity index Δφ and the relative refractive index difference Δ⁺ of the DCF in each of the optical transmission lines having respective span lengths of 50 km, 80 km, and 100 km. As can be seen from this graph, the contribution of DCF reduces as the span length elongates. Namely, as the span length elongates, the contribution of SMF inherently having a low nonlinearity increases, whereby the equivalent effective area EA_(eff) (indicative of relative nonlinearity with respect to DSF (assuming a Non-Zero Dispersion-Shifted Optical Fiber) in the optical transmission line as a whole increases. In FIG. 28, curves G2810, G2820, and G2830 indicate results of calculation concerning the optical transmission lines having span lengths of 50 km, 80 km, and 100 km, respectively.

The optimal Δ⁺ in DCF upon changing the span length will now be explained. FIGS. 29A, 29B, and 29C are graphs showing the relationships between Δφ relative value and Δ⁺ of DCF at each standard in the optical transmission lines having respective span lengths of 50 km, 80 km, and 100 km when the gain by Raman amplification is fixed. In FIGS. 29A to 29C, curves G2911, G2912, and G2913; curves G2921, G2922, and G2923; and curves G2931, G2932, and G2933 indicate results of calculation when Raman gain is 0 dB, 7 dB, and 10 dB, respectively. The ordinate of each graph is the Δφ relative ratio (yielding the lowest nonlinearity when minimized) defined by the following expression (8):

Δφrelative ratio=10log(Δφ/Δφmax)  (8)

The optimal Δ⁺ (at which the Δφ relative ratio is minimized) of DCF at a span length of 50 km is 1.6% from FIG. 29A, the optimal Δ⁺ of DCF at a span length of 80 km is 1.5% from FIG. 29B, and the optimal Δ⁺ of DCF at a span length of 100 km is 1.4% from FIG. 29C, whereby it is seen that the optimal Δ⁺ decreases as the span length is longer (the optimal Δ⁺ depends on distance) regardless of whether Raman amplification exists or not. From these results, when the span length becomes longer, the optimal Δ⁺ is 1.4±0.2% if the fluctuation range is 10% or less, i.e., if the Δφ relative ratio is 0.4 dB or less, and preferably 1.4±0.1% if the fluctuation range is 5% or less, i.e., if the Δφ relative ratio is 0.2 dB or less. These results are applicable not only to optical transmission lines in which a DCF having a W-shaped refractive index profile such as the one shown in FIGS. 6A and 6B is employed, but also to those in which a DCF having an increased number of cladding regions, e.g., a triple or quadruple cladding type refractive index profile, is employed.

Next, the following explains characteristics of each of thirty-first to forty-sixth samples of the optical transmission line according to the present invention.

FIG. 30 is a table showing characteristics at a wavelength of 1550 nm of an A_(eff)-enlarged PSCF employed as the SMF of each of thirty-first to forty-sixth samples of the optical transmission line according to the present invention. The A_(eff)-enlarged PSCF to be employed has a non-intentionally doped core region and has, as characteristics at the wavelength of 1550 nm, a chromatic dispersion of 20.4 ps/nm/km, a dispersion slope of 0.060 ps/nm²/km, a transmission loss of 0.170 dB/km, an effective area A_(eff) of 110 μm², and a nonlinear refractive index N2 of 2.8×10⁻²⁰ m²/W.

Also, FIG. 31 is a table showing characteristics at a wavelength of 1550 nm of samples (DCF10-DCF25) of a dispersion compensating Fiber employed to the optical transmission line according to the present invention. FIG. 31 shows, regarding to DCF10 to DCF25, chromatic dispersion (ps/nm/km), dispersion slope (ps/nm²/km), transmission loss (dB/km), effective area A_(eff) (μm²), nonlinear refractive index N2 (×10⁻²⁰ m²/W), and bending loss (dB/m), successively from the left side. Of the dispersion compensating fibers of DCF10 to DCF 25, DCF10 to DCF13 are included in a first group with the effective area A_(eff) of 23 μm², DCF14 to DCF17 are included in a second group with the effective area A_(eff) of 25 μm², DCF18 to DCF21 are included in the third group with the effective area A_(eff) of 31 μm², and DCF22 to DCF25 are included in a fourth group with the effective area A_(eff) of 33 μm².

Further, FIG. 32 is a table showing characteristics at a wavelength of 1550 nm of each of thirty-first to forty-sixth samples of the optical transmission line according to the present invention. Each of the thirty-first to forty-sixth samples of the optical transmission line according to the present invention comprise the associated one of DCFs fusion-spliced to A_(eff)-enlarged PSCF, respectively. In other words, the thirty-first to thirty-fourth samples respectively comprise the associated one of DCF10 to DCF13 (including first group) having the effective area A_(eff) of 23 μm² and the A_(eff)-enlarged PSCF, the thirty-fifth to thirty-eighth samples respectively comprise the associated one of DCF14 to DCF17 (including second group) having the effective area A_(eff) of 25 μm² and the A_(eff)-enlarged PSCF, the thirty-ninth to forty-second samples respectively comprise the associated one of DCF18 to DCF21 (including third group) having the effective area A_(eff) of 31 μm² and the A_(eff)-enlarged PSCF, and the forty-third to forty-sixth samples respectively comprise the associated one of DCF22 to DCF25 (including fourth group) having the effective area A_(eff) of 33 μm² and the A_(eff)-enlarged PSCF. FIG. 32 shows, regarding to thirty-first to forty-sixth samples, average chromatic dispersion (ps/nm/km), average dispersion slope (ps/nm²/km), equivalent effective area EA_(eff) (μm²), SMF length (km), and DCF length (km), successively from the left side. Each of the samples has a span length of 50 km.

The graph showing relationships between the average dispersion slope S_(ave) and equivalent effective area EA_(eff) in thirty-first to forty-sixth samples is shown in FIG. 33. In FIG. 33, a curve G3310 shows thirty-first to thirty-fourth samples respectively including DCF10 to DCF13 (each having A_(eff) 23 μm²), a curve G3320 shows thirty-fifth to thirty-eighth samples respectively including DCF14 to DCF17 (each having A_(eff) 25 μm²), a curve G3330 shows thirty-ninth to forty-second samples respectively including DCF18 to DCF21 (each having A_(eff) 31 μm²), and a curve G3330 shows forty-third to forty-sixth samples respectively including DCF22 to DCF25 (each having A_(eff) 33 μm²)

The curve G3310 of FIG. 33 corresponds to the lower limit f(S_(ave)) of equivalent effective area EA_(eff), and the curve G3340 of FIG. 33 also corresponds to the upper limit g(S_(ave)) of equivalent effective area EA_(eff). By respectively fitting the curves 3310 and 3330 to linear functions, the curves 3310 and 3330 can be defined as the following expressions (9) and (10):

EA _(eff)=941.64×S _(ave)+76.168  (9)

EA _(eff)=885.48×S _(ave)+91.208  (10)

On the other hand, FIG. 34 is a graph showing the relationship between span length L (km) and equivalent effective area EA_(eff), regarding to thirty-first to forty-sixth samples of the optical transmission line according to the present invention. The curve of FIG. 34 shows a span length dependency of equivalent effective area EA_(eff), and the linear fitting function of the curve can be defined as the following expression (11):

EA _(eff)=0.6093×L+42.026  (11)

The above expressions (9) and (10) are obtained at the condition while the span length L of each sample in FIG. 33 is 50 km. That is, the lower limit f(S_(ave)) can be defined as the following expression (12):

f(S_(ave))=942×S _(ave)+76.168+0.6093×(L−50)=942×S _(ave)+0.609×L+45.7  (12)

while using the average dispersion slope S_(ave) and the span length L as variable.

Additionally, the upper limit g(S_(ave)) can be defined as the following expression (13):

g(S _(ave))=885.48×S _(ave)+91.208+0.6093×(L−50)=885×S _(ave)+0.609×L+60.7  (13)

while using the average dispersion slope S_(ave) and the span length L as variable.

As described above, on thirty-first to forty-six samples of the optical transmission line according to the present invention, the lower limit f(S_(ave)) and the upper limit g(S_(ave)) of the equivalent effective area EA_(eff) are respectively defined by the above-mentioned expressions (12) and (13).

As in the foregoing, employed as a repeatered transmission line according to the present invention is an optical transmission line having a structure in which a single-mode optical fiber and a dispersion-compensating optical fiber are fusion-spliced to each other and exhibiting, as characteristics at the wavelength of 1550 nm, an average dispersion slope S_(ave) of −0.0113 ps/nm²/km or more but 0.0256 ps/nm²/km or less, and an equivalent effective area EA_(eff) of 50 μm² or more, wherein the average dispersion slope S_(ave) and the equivalent effective area EA_(eff) are designed so as to satisfy a predetermined condition such that the bending loss becomes 2 dB/m or more but 10 dB/m or less. As a consequence, both the nonlinearity and average dispersion slope of the optical transmission line are lowered, which enables high-speed, large-capacity WDM transmissions at a high bit rate (10 Gbits/s) over a wide wavelength band (e.g., from 1530 nm to 1600 nm).

From the invention thus described, it will be obvious that the embodiments of the invention may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended for inclusion within the scope of the following claims. 

What is claimed is:
 1. An optical transmission line for a repeatered transmission line having a span length of L disposed between stations, said optical transmission line comprising a single-mode optical fiber and a dispersion-compensating optical fiber, said single-mode optical fiber having a zero-dispersion wavelength in a 1.3-μm wavelength band, said dispersion-compensating optical fiber being disposed at a position where signals outputted from said single-mode optical fiber reach and compensating for a chromatic dispersion of said single-mode optical fiber; said optical transmission line as a whole having an average dispersion slope S_(ave) of −0.0113 ps/nm²/km or more but 0.0256 ps/nm²/km or less at a wavelength of 1550 nm, and an equivalent effective area EA_(eff) of 50 μm² or more at the wavelength of 1550 nm; said average dispersion slope S_(ave) and said equivalent effective area EA_(eff) satisfying the relationship of: f(S_(ave))≦EA _(eff) ≦g(S _(ave)) where f(S_(ave)) is a lower limit function which yields the lower limit of EA_(eff) by the expression: 942×S _(ave)+0.609×L+45.7 while using the average dispersion slope S_(ave) and the span length L as variable, and g(S_(ave)) is an upper limit function which yields the upper limit of EA_(eff) by the expression: 885×S _(ave)+0.609×L+60.7 while using the average dispersion slope S_(ave) and the span length L as variable.
 2. An optical transmission line according to claim 1, wherein said optical transmission line as a whole has an average transmission loss of 0.185 dB/km or more but 0.210 dB/km or less at the wavelength of 1550 nm.
 3. An optical transmission line according to claim 1, wherein said optical transmission line as a whole has an average transmission loss of 0.185 dB/km or more but 0.220 dB/km or less within the wavelength band from 1530 nm to 1600 nm.
 4. An optical transmission line according to claim 1, wherein said single-mode optical fiber has an effective area of 100 μm² or more at the wavelength of 1550 nm.
 5. An optical transmission line according to claim 1, wherein said optical transmission line as a whole has a negative average chromatic dispersion at the wavelength of 1550 nm.
 6. An optical transmission system including a plurality of stations, wherein the optical transmission line according to claim 1 is employed as at least one of repeatered transmission lines disposed between said stations.
 7. An optical transmission system including, at least, a transmitting station, one or more repeater stations, and a receiving station, wherein the optical transmission line according to claim 6 is employed as a plurality of repeatered transmission lines adjacent each other among repeatered transmission lines disposed between said stations; and wherein an optical transmission line made of said single-mode optical fiber alone is employed as a repeatered transmission line subsequent to said repeatered transmission lines each having the optical transmission line according to claim 6 employed therein.
 8. An optical transmission system including a plurality of stations, wherein the optical transmission line according to claim 1 is employed as at least one of repeatered transmission lines disposed between said stations, at least one of said stations including a Raman amplifier. 